7.3.9 problem 9

Internal problem ID [49]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 9
Date solved : Friday, February 07, 2025 at 08:13:11 AM
CAS classification : [_separable]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve((1-x^2)*diff(y(x),x)=2*y(x),y(x), singsol=all)
 

\[ y = -\frac {\left (x +1\right ) c_1}{x -1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 22

DSolve[(1-x^2)*D[y[x],x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {c_1 (x+1)}{x-1} \\ y(x)\to 0 \\ \end{align*}